R Notebook

library(tidyverse)
library(modelr)
library(GGally)
library(ggfortify)
library(relaimpo)
library(lm.beta)

MVP 1

# read in dataset
house_data <- read_csv("data/kc_house_data.csv") 

Rows: 21613 Columns: 21
── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr   (1): id
dbl  (19): price, bedrooms, bathrooms, sqft_living, sqft_lot, floors, waterfront, view, condition, grade, sqft_above, sqf...
dttm  (1): date

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# clean dataset
house_tidy <- house_data %>% 
  dplyr::select(-c(date, id, sqft_living15, sqft_lot15, zipcode)) %>% 
  mutate(yr_renovated = ifelse(yr_renovated == 0, FALSE, TRUE)) %>% 
  mutate(waterfront = ifelse(waterfront == 0, FALSE, TRUE)) %>% 
  rename("renovated" = "yr_renovated") %>% 
  mutate(grade = ifelse(grade <= 3, "poor", ifelse(grade <= 7, "average", "good")))
  

MVP 2

# use alias() to check for any variables that lead to an alias
alias(lm(price ~ ., data = house_tidy))

Model :
price ~ bedrooms + bathrooms + sqft_living + sqft_lot + floors + 
    waterfront + view + condition + grade + sqft_above + sqft_basement + 
    yr_built + renovated + lat + long

Complete :
              (Intercept) bedrooms bathrooms sqft_living sqft_lot floors waterfrontTRUE view condition gradegood gradepoor
sqft_basement  0           0        0         1           0        0      0              0    0         0         0       
              sqft_above yr_built renovatedTRUE lat long
sqft_basement -1          0        0             0   0  

# remove sqft_basement
house_tidy <- house_tidy %>% 
  dplyr::select(-sqft_basement)

# rerun alias to check that there are now no aliases
alias(lm(price ~ ., data = house_tidy))

Model :
price ~ bedrooms + bathrooms + sqft_living + sqft_lot + floors + 
    waterfront + view + condition + grade + sqft_above + yr_built + 
    renovated + lat + long

MVP 3

ggpairs(house_tidy_numeric)

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ggpairs(house_tidy_nonnumeric)

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1st Predictor

# first model price ~ sqft_living
mod_1 <- lm(price ~ sqft_living, data = house_tidy)

summary(mod_1)

Call:
lm(formula = price ~ sqft_living, data = house_tidy)

Residuals:
     Min       1Q   Median       3Q      Max 
-1476062  -147486   -24043   106182  4362067 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -43580.743   4402.690  -9.899   <2e-16 ***
sqft_living    280.624      1.936 144.920   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 261500 on 21611 degrees of freedom
Multiple R-squared:  0.4929,    Adjusted R-squared:  0.4928 
F-statistic: 2.1e+04 on 1 and 21611 DF,  p-value: < 2.2e-16

par(mfrow = c(2, 2))
plot(mod_1)

# second model price ~ sqft_above
mod_2 <- lm(price ~ sqft_above, data = house_tidy)

summary(mod_2)

Call:
lm(formula = price ~ sqft_above, data = house_tidy)

Residuals:
    Min      1Q  Median      3Q     Max 
-913132 -165624  -41468  109327 5339232 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  59953.2     4729.8   12.68   <2e-16 ***
sqft_above     268.5        2.4  111.87   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 292200 on 21611 degrees of freedom
Multiple R-squared:  0.3667,    Adjusted R-squared:  0.3667 
F-statistic: 1.251e+04 on 1 and 21611 DF,  p-value: < 2.2e-16

par(mfrow = c(2, 2))
plot(mod_2)

sqft_living will be used as the first predictor since the r2 value is higher, 50% vs 36%, diagnostics for both models look ok-ish but not great!

Second predictor

prestige_remaining_resid %>%
  ggpairs(aes(colour = waterfront, alpha = 0.5))

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mod_3 <- lm(price ~ sqft_living + yr_built, data = house_tidy)

summary(mod_3)

Call:
lm(formula = price ~ sqft_living + yr_built, data = house_tidy)

Residuals:
     Min       1Q   Median       3Q      Max 
-1684544  -137797   -20753   105703  4036827 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.546e+06  1.206e+05   37.69   <2e-16 ***
sqft_living  3.046e+02  1.977e+00  154.03   <2e-16 ***
yr_built    -2.354e+03  6.183e+01  -38.07   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 253100 on 21610 degrees of freedom
Multiple R-squared:  0.5247,    Adjusted R-squared:  0.5247 
F-statistic: 1.193e+04 on 2 and 21610 DF,  p-value: < 2.2e-16

par(mfrow = c(2, 2))
plot(mod_3)

mod_4 <- lm(price ~ sqft_living + lat, data = house_tidy)

summary(mod_4)

Call:
lm(formula = price ~ sqft_living + lat, data = house_tidy)

Residuals:
     Min       1Q   Median       3Q      Max 
-1487994  -125643   -20309    84613  4368717 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -3.416e+07  5.653e+05  -60.44   <2e-16 ***
sqft_living  2.749e+02  1.794e+00  153.27   <2e-16 ***
lat          7.177e+05  1.189e+04   60.36   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 241900 on 21610 degrees of freedom
Multiple R-squared:  0.566, Adjusted R-squared:  0.566 
F-statistic: 1.409e+04 on 2 and 21610 DF,  p-value: < 2.2e-16

par(mfrow = c(2, 2))
plot(mod_4)

Second predictor will be lat as it gives a slight higher r2 value, 56% vs 52% for yr_built. The diagnostics are almost identical.

Third predictor

prestige_remaining_resid <- house_tidy %>%
  add_residuals(mod_4) %>%
  dplyr::select(-c("price", "sqft_living", "lat"))

prestige_remaining_resid %>%
  ggpairs(aes(colour = waterfront, alpha = 0.5))

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mod_5 <- lm(price ~ sqft_living + lat + view, data = house_tidy)

summary(mod_5)

Call:
lm(formula = price ~ sqft_living + lat + view, data = house_tidy)

Residuals:
     Min       1Q   Median       3Q      Max 
-1596893  -115223   -14728    82111  4327282 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -3.438e+07  5.363e+05  -64.11   <2e-16 ***
sqft_living  2.502e+02  1.775e+00  140.93   <2e-16 ***
lat          7.228e+05  1.128e+04   64.08   <2e-16 ***
view         1.042e+05  2.125e+03   49.05   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 229400 on 21609 degrees of freedom
Multiple R-squared:  0.6095,    Adjusted R-squared:  0.6094 
F-statistic: 1.124e+04 on 3 and 21609 DF,  p-value: < 2.2e-16

par(mfrow = c(2, 2))
plot(mod_5)

mod_6 <- lm(price ~ sqft_living + lat + yr_built, data = house_tidy)

summary(mod_6)

Call:
lm(formula = price ~ sqft_living + lat + yr_built, data = house_tidy)

Residuals:
     Min       1Q   Median       3Q      Max 
-1645242  -120261   -14570    85543  4077885 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -2.770e+07  5.929e+05  -46.72   <2e-16 ***
sqft_living  2.936e+02  1.861e+00  157.79   <2e-16 ***
lat          6.551e+05  1.182e+04   55.40   <2e-16 ***
yr_built    -1.787e+03  5.875e+01  -30.42   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 236900 on 21609 degrees of freedom
Multiple R-squared:  0.5838,    Adjusted R-squared:  0.5838 
F-statistic: 1.011e+04 on 3 and 21609 DF,  p-value: < 2.2e-16

par(mfrow = c(2, 2))
plot(mod_6)

For the third predictor we will choose view over lat as it provide the higher r2 value.

Forth predictor

house_resid <- house_tidy %>% 
  add_residuals(mod_5) %>% 
  dplyr::select(-price)

coplot(resid ~ sqft_living | lat, 
       panel = function(x, y, ...){
         points(x, y)
         abline(lm(y ~ x), col = "blue")
       }, 
       data = house_resid, 
       columns = 6)

coplot(resid ~ lat | view, 
       panel = function(x, y, ...){
         points(x, y)
         abline(lm(y ~ x), col = "blue")
       }, 
       data = house_resid, 
       columns = 6)

coplot(resid ~ sqft_living | view, 
       panel = function(x, y, ...){
         points(x, y)
         abline(lm(y ~ x), col = "blue")
       }, 
       data = house_resid, 
       columns = 6)